Abstract

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases.Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications, such as digital twins. We present a  low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling, implemented as a simulation in the CompuCell3D simulation environment. The Furth equation, the usual characterization of mean squareddisplacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movementtransitions from a ballistic to a diffusive regime. Experiments have shown that for short time intervals, cells exhibit anadditional fast diffusive regime. Our simulations’ MSD curves reproduce the three experimentally observed temporal regimes,with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time interval-ballistic motion.The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time and lengthscales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisonsamong MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulationsreplicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneouscell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. We also propose and validate a migratory  polarization definition as a proxy to predict cell displacement. Chemotaxis is simulated as an external stimulus to polarization orientation and not as an external force acting on the cell. Finally, we propose a stochastic model and its anlytical and numeric solution that describes well out findings. Comparisonsbetween experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer timecell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations,including chemotaxis, migration through complex 3D matrices, and collective cell motion.